JCPenney CEO Ron Johnson is mounting a radical overhaul of the flailing department-store chain — but that doesn’t mean he’s stuck at the office on nights and weekends.

Over the past year, the former Apple exec only rarely spends a full work week at the retailer’s headquarters in Plano, Texas, sources told The Post.

“He’s there four days a week, if that much,” according to one source close to the company.

Commuting on a company jet from his home in Palo Alto, Calif., sources say Johnson stays during the week at Dallas’s swanky Ritz-Carlton hotel — a perk subsided by the company.

That’s in sharp contrast to Penney’s two previous CEOs, Allen Questrom and Mike Ullman, who took up permanent residence in Dallas and consistently worked long hours at the office.

“What does [Johnson] do the rest of the time?” one former exec asked. “If he’s doing this huge transformation, why isn’t he there 12 hours a day helping everybody get things done?”

Penney officials didn’t respond to requests for comment yesterday.

Johnson isn’t the only one skirting face time, sources said. Hundreds of workers at the Plano headquarters have begun showing up later for work and clocking out earlier, sources said.

“They used to be in the office at 7:30 in the morning, and they’d be calling you to get things done,” said an executive at one major Penney supplier. “Now, they’re rolling in at 8:30 or 9. If I got a 9:30 meeting with them, I’d be shocked.”

Instead of leaving at 5 or 5:30 p.m., sources said, the same workers now are routinely leaving at 4:30 — despite being saddled with more work in the wake of thousands of firings since Johnson took the helm in 2011.

As reported by The Post, Johnson this month plans to lay off as much as 10 percent of the 3,000 or so workers who remain at the Plano offices.

Sources said Johnson, who has sought to dismantle Penney’s once-regimented corporate culture, hasn’t moved to stop the slacking. While the casual, Silicon Valley-style approach may have led to success at Apple, some insiders say it’s a bad fit for Penney’s complex, data-driven supply chain.

“This is a big retailer where a lot of different things need to be done every day at a certain time,” one insider said, noting that inventory management is growing spotty, even as Johnson seeks to bring back sales events that are more difficult to execute.

While Johnson may be hard at work when he’s away, sources said his secretive habits have usually left his activities and whereabouts murky to all but a handful of top officers and trusted confidants.

Nick Wooster, a former Bergdorf-Goodman exec who is now in charge of Penney’s private-label merchandise, is also being put up at the Ritz, sources said. Typically arriving in Plano Monday morning, Wooster usually heads back to his home in New York late Thursday or early Friday, sources said.

“He always says he’s got meetings with the design team,” one insider said of Wooster, noting that Penney has opened a design office in SoHo. “Pretty convenient that it’s always on a Friday.”

Even Michael Francis, a former Target exec who was booted from Penney last summer, remained in his home state of Minnesota during his eight-month stint — despite the fact he was president of the company, sources said.

“If [Francis] wasn’t going to come down to Plano, they’d fly personal assistants up to Minneapolis to accommodate him,” according to one source.